By total differentiation, determine or find the approx. change in the length of the hypotenuse of a right triangle when its legs change from 3 ft and 4 ft to 3.2 ft and 3.9 ft, respectively.

Q: The equation y2(y² – 4) = x²(x² - 5) is known as the devil's curve. Give an equation for the tangent…

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Q: The volume V of a right circular cylinder is given by the formula V= Tr h, where r is the radius and…

A: Given that the volume V of a right circular cylinder is given by the formula V =(pi)r2h, where r is…

Q: A triangle is inscribed in a parabola such that the first vertex (point A) is at the origin and the…

A: This question can be solved using the concept of maxima and minima.

Q: Let C(x)= x2+4x+1 dollars be the cost function, where the x represents the quantity. The estimate…

A: Cost

Q: If f (x) >0 and f (x)< 0 for all x over a given part of the domain of a function f, then the graph…

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Q: 24. Given z = 6x°y-e", calculate or z. A) 12y–x'e" B) 12y-ye" C) 12y-e" ху D) 12x - хуе"

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Q: 2. Describe in word all transformations involved. y = -3sin(180° – 4x) + 5

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Q: Use the cross product and determine the volume of the parallelepiped generated by the three vectors…

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Q: Find the area, A, of the region enclosed by the cardioid r = 8+ 8 cos 0. 96 л (B 52 A © 48 n (D) 100…

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Q: Find dy/dx: solution in handwritten 1. y = 5* (** + dx VE х4 3 -x²,

A: Using leibnitz rule for integral.

Q: 4.lim 1252x-7+2 Sーズ 5. lim e*+1 X-4

A: Let's find.

Q: For the following function f, find the antiderivative F that satisfies the given condition. 3 f(v) =…

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Q: Use the limit definition to compute the derivative of the function f(x) = Vx + 2 at x = 1. (Use…

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Q: 1) Evaluate lim 10 VX-5 X-25 x25

A: We can find the limit as below.

Q: Question Suppose that you are estimating sin (0.3) using the third Maclaurin polynomial for sin (x).…

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Q: consider a function f (x) vihose derivative f"(x) is continuous as shown belowr. Graph of f'(x), NOT…

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Q: Sketch the graph the integrands and use areas to evaluate the integrals. 1. L'lx| dx Sketch the…

A: The graph is shown below, where the shaded region represents the area.

Q: Find the derivative of the function: f(x) = [sin(4x + x)] [cos(x4 + 4)] f(x) = e3x²+*(cscx + secx)2…

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Q: 5. [4 log x + 1] dx

A: Student has specifically asked for the solution to the Question (5). Hence answer to that problem is…

Q: Name:Y Varner 1. Find the antiderivative of the function |4x – 2x² + x – 5 dx Jar - 20* 2. Evaluate…

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Q: Sketch the graph of the cardioid r = 1 + cosθ and the circle r = 3cosθ. Shade the region that is…

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Q: The triple integral SLS (x+2y – 2)dxdydz is equal to -8 -1

A: This can be solved as follows:

Q: Using the Optimization in Derivatives, solve the following problem: A 150-room hotel in Reno will…

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Q: Determine the direction vector of the following lines where lz is in 3D a) l1:2x – 3y + 6 = 0 %3D -…

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Q: gas is escaping a spherical ballon at the rate of 4cm per minute . how fast is the surface area…

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Q: If å is a vector in the direction of S60°E, then draw its opposite vector and state the direction

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Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

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Q: Sketch the graph the integrands and use areas to evaluate the integrals. | Ix| dx -2

A: Follow the procedure given below.

Q: x+2x2-3x x²+4x+3 2) Evaluate lim -6-1. x→ -3 Show every step.

A: We can solve this as follows:

Q: Consider the series n+5 Determine whether the series converges, and if it converges, determine its…

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Q: Find the Laplace transform of sint 0<t<27 f() =

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Q: Select the conic section represented by the equation. 13x 2 + 5y 2 - 6x + 3y - 5 = 0 circle point…

A: We can select the conic section as below.

Q: / Solve the following differential equation: e2y dx + 2(xe2y – y)dy = 0 -

A: To solve the given differential equation.

Q: 4n – 9 5n + 4 S - Given that sequence {an} = { (а) Show that the sequence is monotonically…

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Q: Postal regulations require that for a rectangular package with a square base, the perimeter of the…

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Q: Evaluate y' of the given functions y = /3x + 4)(x + 3)

A: We can find the derivative as below.

Q: determine which statement is true {(x,y)|y=√9-4x2} (A) not a function (B) function; domain: [-3/2…

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Q: (4) Evaluate S SR e™y-2dA where R is the region enclosed by y = 4x, y = }, y = ± and y = 1.

A: Let's find.

Q: 00 n³n² COS 5n³ +3, 1

A: See the answer below

Q: determine which statement is true   x + 2y^2 + 20 = 0 (A) not a function (B) function; domain: R…

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Q: d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

A: ddtr1(t).r2(t)=r2(t)dr1(t)dt+r1(t)dr2(t)dt ddtr1(t)×r2(t)=r1(t)×dr2(t)dt+dr1(t)dt×r2(t)

Q: Conics Find the equation of a parabola that has focus at (-4,0) and directrix x= 2

A: A detailed solution is given below

Q: Sketch the graph the integrands and use areas to evaluate the integrals. + dx -2

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Q: Solve the linear differential equation dy 2y x2 - dx 1+x2 x2 y = x² tan-1(x) + c y = + c 1+x2 Option…

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Q: Directions: Solve the following using the theorems on differentiation. 1. Evaluate x5dx 2. Evaluate…

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 10xe…

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Q: TOPIC: OPTIMIZATION IN DERIVATIVES Directions: Read and analyze each problem carefully and solve for…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) dy =

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Q: What is the area enclosed by the curve r = 2 cos 30? Answer is in square units. Use two (2) decimal…

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Q: (cos 2x) f (x) = e

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